Ernest's friend rolls a six-sided number cube and lands on square 8. She asks Ernest to guess what number she rolled. He guesses that she rolled a 3. She says he's wrong.

Ernest wonders if she could have rolled a number other than 3. Use a mapping diagram to help guess what number she rolled.

If she would have rolled

Create a Mapping Diagram

When playing this game, the square you land on during the first turn depends on the number you roll. You can write this as a function: SQUARE(number), or S(n). For example, if you roll a 2, you end up on square 2 (when you land on 3 you move back a space). So S(2) = 2.

1. Describe the possible inputs of S(n) using words. (2 points: 1 point for the description, 1 point for the list of numbers)

2. Describe the possible outputs of S(n) using words. (1 point)

3. Draw a mapping diagram for S(n) that maps all the possible inputs and outputs for a player's first turn. Note that the player should begin on square 1. (6 points: 3 points for the inputs and outputs, and 3 points for the mapping)

4. In the mapping diagram you created, what numbers are in the domain of S(n)? Explain what this means. (2 points: 1 point for the domain, 1 point for the explanation)

5. What numbers are in the range of S(n)? Explain what this means. (2 points: 1 point for the range, 1 point for the explanation)

Evaluate the Conjecture

6. Based on the mapping diagram, is it possible that the player rolled a number other than 3 to land on square 8? If so, which number or numbers? Explain your answer. (2 points: 1 point for the answer, and 1 point for the explanation)

Defining Functions
7. Does the mapping diagram you created for S(n) for the first turn of the game represent a function? Why or why not? (2 points: 1 point for the answer, and 1 point for the explanation)